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Ex 13.1, 31 - If function f(x) lim x->1 f(x)-2/x2-1 = pi - Ex 13.1

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  1. Chapter 13 Class 11 Limits and Derivatives
  2. Serial order wise
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Ex 13.1, 31 If the function f(x) satisfies lim﷮x → 1﷯ 𝑓 𝑥﷯ − 2﷮𝑥2 − 1﷯ = π , evaluate lim﷮x→1﷯ f(x) . Given lim﷮x→1﷯ 𝑓 𝑥﷯ − 2﷮ 𝑥﷮2﷯ − 1﷯ = π lim﷮x→1﷯ 𝑓 𝑥﷯−2﷮ lim﷮x→1﷯ (𝑥﷮2﷯−1) ﷯ = π lim﷮x→1﷯ (f(x) – 2) = π × lim﷮x→1﷯ (x2 – 1) lim﷮x→1﷯ f(x) – lim﷮x→1﷯ 2 = π ( lim﷮x→1﷯ x2 – lim﷮x→1﷯ 1) Finding limits, putting x = 1 lim﷮x→1﷯ f(x) – 2 = π × ((1)2 – 1) lim﷮x→1﷯ f(x) – 2 = π × 0 lim﷮x→1﷯ f(x) – 2 = π × 0 lim﷮x→1﷯ f(x) – 2 = 0 lim﷮x→1﷯ f(x) = 2 Thus 𝒍𝒊𝒎﷮𝐱→𝟏﷯ f (x) = 2

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